Mean-field equilibrium price formation under single-default risk

Battle Count: 99

The paper provides a theoretical framework for understanding how default risk is priced in equilibrium in large-population markets. While not directly applicable to algorithmic trading strategies, it offers insights into the decomposition of risk premia (Brownian hedging vs. default-risk components), which is relevant for credit risk modeling, defaultable bond pricing, and understanding market microstructure under default events. The quantitative characterization of how default intensity, jump size, and agent heterogeneity shape equilibrium premia could inform trading strategies in credit markets.

The paper requires advanced knowledge of stochastic analysis (BSDEs with quadratic growth, compensated jump martingales, BMO spaces), mean-field game theory, PDE theory (coupled semilinear parabolic systems, Sobolev spaces, Krylov estimates), and mathematical finance (martingale optimality principle, Girsanov theorem, Doléans-Dade exponentials). The fixed-point construction involves both a scalar contraction map and a BSDE contraction on a Markovian function space. No code or numerical implementation is provided. Reproducing the theoretical results requires deep expertise in multiple advanced mathematical disciplines.

The paper is a fully self-contained theoretical work with complete mathematical proofs. All assumptions, definitions, lemmas, and theorems are rigorously stated and proved. No numerical experiments or code are provided, but the mathematical arguments are verifiable. The Markovian factor model and PDE system are explicitly specified, enabling independent verification of the fixed-point construction.